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Is there a general way to visualize the space curve defined by the intersection of 2 implicitely defined surfaces?

I know, this has been discussed here before with the following suggested solutions:

1. Visualize all equations in the same plot - this has the disadvantage that surfaces - even if opaque, distract attention and may obstruct the view on the intersection curves

2. Combine the defining equations into a system of euations and solve it, present the solutions as parametric plots - this doesn't work with complex surfaces where Sage cannot solve the system.

I know, some 3D objects have an intersection() method, but apparently not those generated by implicit_plot3d. But maybe, someone has another solution?

Is there a general way to visualize the space curve defined by the intersection of 2 implicitely defined surfaces?

I know, this has been discussed here before with the following suggested solutions:

1. Visualize all equations in the same plot - this has the disadvantage that surfaces - even if opaque, distract attention and may obstruct the view on the intersection curves

2. Combine the defining equations into a system of euations and solve it, present the solutions as parametric plots - this doesn't work with complex surfaces where Sage cannot solve the system.

I know, some 3D objects have an intersection() method, but apparently not those generated by implicit_plot3d. But maybe, someone has another solution?